Reputation and bounded memory in repeated games with incomplete information

This dissertation is a study of bounded memory and reputation in games. In the first chapter we show that the optimal use of a finite memory may induce inertia and infrequent updating on a player's behavior, sometimes for strategic reasons. The setting is a repeated cheap-talk game with incomplete information on the sender's type. The receiver has only a fixed number of memory states available. He knows that he is forgetful and his strategy is to choose an action rule, which is a map from each memory state to the set of actions, and a transition rule from state to state. Unlike in most models of bounded memory, we view memory as a conscious process: in equilibrium strategies must be consistent with beliefs. First, we show that the equilibrium transition rule will be monotonic. Second, we show that when memory constraints are severe, the player's transition rule will involve randomization before he reaches the extreme states. In a game, randomization has two interpretations: it is used as a memory-saving device and as a screening device (to test the opponent before updating).; The second chapter shows that bounded memory with sequential rationality constraints can explain long-run reputation even in the case of parties with opposite interests. Memory is modeled as a finite set of states. The strategy of the player is an action rule, which is a map from memory to actions, and a transition rule from state to state. In equilibrium, strategies and beliefs must be consistent. The setting is an infinitely repeated game with one-sided incomplete information. The informed player is either a zero-sum normal type or a commitment type playing a mixed strategy. Under full memory, types are revealed asymptotically. Bounded memory in the form of a finite automata cannot, by itself, explain long-run reputations, as we show in the paper. However, if memory is modeled as a conscious process with sequential rationality constraints, then long-run reputation will be sustained in any Markovian equilibrium.; In the third chapter we study a repeated adverse selection model in which the best contract for the principal is to reproduce the outcome with sequential rationality constraints. The model suggests that contracting will only have an impact when the adverse selection problem is less severe.